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zepelin [54]
2 years ago
15

When Ximena commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 38 minutes and a

standard deviation of 4.5 minutes. Using the empirical rule, determine the interval that represents the middle 68% of her commute times.
Mathematics
1 answer:
irga5000 [103]2 years ago
6 0

Answer:

The interval that represents the middle 68% of her commute times is between 33.5 and 42.5 minutes.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 38 minutes, standard deviation of 4.5 minutes.

Determine the interval that represents the middle 68% of her commute times.

Within 1 standard deviation of the mean. So

38 - 4.5 = 33.5 minutes

38 + 4.5 = 42.5 minutes.

The interval that represents the middle 68% of her commute times is between 33.5 and 42.5 minutes.

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